Re: Partial Differential Equation

*To*: mathgroup at smc.vnet.net*Subject*: [mg26660] Re: Partial Differential Equation*From*: "Kevin J. McCann" <KevinMcCann at home.com>*Date*: Wed, 17 Jan 2001 00:47:16 -0500 (EST)*References*: <93r7gq$4q4@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Philippe, The problem you have posed is a 2-point boundary value problem which Mathematica often has difficulty with. The solution is to turn it into a one-point BVP, and find the initial condition on T(0) that gives the desired T'(1). The technique is often called a shooting technique. I have sent you a NB separately that gives my attempt. Cheers, Kevin The wise words of P. Poinas on 13 Jan 2001 22:47:38 -0500: > Dear Group, > > I am trying to solve the following problem: > > \!\(\(\(NDSolve[{\(T''\)[R] + \((1/\((R + 0.05)\))\)\ \(T'\)[R] - > 10\^\(-8\)\ \ T[R]\^4 == 0, \(T'\)[0] == \(-0.07\), \ > \(T'\)[1] == > 0}, \ T, \ {R, \ 0, \ 1}]\)\(\ \)\)\) > > and I get the following message: > > NDSolve::"inrhs": "Differential equation does not evaluate to a number > or the \ > equation is not an nth order linear ordinary differential equation." > > I know that this error is because I am defining the derivative at 2 > different R values: > > at R=0, T'[0 ]= -0.07 > and R=1, T'[1] = 0 > > hence it is not an initial boundary condition. > > 1) How can I turn around the problem? > > > Actually, I found the Mathematica Book (V4) very weak on the subject. In > page 924, it seems possible in In[7] to find a solution to a linear > differential equation, even with 2 boundary conditions defined at 2 > different x values! My problem being not linear cannot therefore be > solved. But Mathematica does not mentioned the linearity as a show > stopper. > > 2) Does anybody know a better description of Mathematica's capacity? > > Thank you for helping me, > > > Philippe Poinas > >